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This is the second and considerably extended edition of the book of the same authors published in 1987. The applied style of presentation has not changed. But important developments on topics like Boolean models, stereology, random tesselations, Gibbs processes and random shapes have been added. The book covers a large variety of ideas and models which are used in stochastic geometry and also gives an introduction to the statistical analysis of these models. Applications of these models are numerous in several fields e.g. in geology, material sciences, biological models of tissues, agriculture, landsat data. The origin of this field is to find in the problem to recover information on threedimensional structures when only information on one-or two-dimensional sections is available.From this origin a rich field of science has emerged. The book describes underlying general concepts like point processes, random sets and random measures and gives an introduction to the most prominent special models like Poison processes, hard-core and Gibbs-processes, the Boolean-model, fibre and surface processes and the Voronoitesselation.The main aim of the book is to make these developments available to the applied scientist and at the same time to give a mathematical exact exposition including the recent and relevant research.As consequence of this concept the level of exposition is uneven. In some parts the explanations are heuristic or by examples and often without detailed mathematical proofs. But the reader gets a unique introduction and perspective of the potential use of the models and the underlying basic mathematical concepts. In its kind there is no equally informative and readable exposition. L. R~SCHENDORF

This paper proposes an approximative method for maximum likelihood estimation of parameters of Neyman-Scott and similar point processes. It is based on the point pattern resulting from forming all difference points of pairs of points in the window of observation. The intensity function of this constructed point process can be expressed in terms of second-order characteristics of the original process. This opens the way to parameter estimation, if the difference pattern is treated as a non-homogeneous Poisson process. The computational feasibility and accuracy of this approach is examined by means of simulated data. Furthermore, the method is applied to two biological data sets. For these data, various cluster process models are considered and compared with respect to their goodness-of-fit.

This paper describes two algorithms for the generation of random packings of spheres with arbitrary diameter distribution. The first algorithm is the force‐biased algorithm of Mościński and Bargieł. It produces isotropic packings of very high density. The second algorithm is the Jodrey‐Tory sedimentation algorithm, which simulates successive packing of a container with spheres following gravitation. It yields packings of a lower density and of weak anisotropy. The results obtained with these algorithms for the cases of log‐normal and two‐point sphere diameter distributions are analysed statistically, i. e. standard characteristics of spatial statistics such as porosity (or volume fraction), pair correlation function of the system of sphere centres and spherical contact distribution function of the set‐theoretical union of all spheres are determined. Furthermore, the mean coordination numbers are analysed. These results are compared for both algorithms and with data from the literature based on other numerical simulations or from experiments with real spheres.

Termite mounds are a widespread feature in most African savannas. These structures exhibit high nutrient contents and often host a special vegetation composition. In this study, we analysed mound distribution patterns of a fungus-growing termite species, Macrotermes michaelseni, an important ecosystem engineer in the savannas of Namibia. Inhabited mounds taller than 0.7 m were regularly distributed. We view this pattern as a result of intraspecific competition. The heights of mounds taller than 0.7 m were correlated positively with their distance, such that mounds closer together, i.e. up to inter-mound distances of approximately 50 m, tended to be smaller than average. This indicates that intraspecific competition for foraging areas controls mound distribution pattern and colony size. Differences between mound heights increased on the spatial scale up to inter-mound distances of 80 m. We assume that the foundation of new colonies is only possible in unoccupied patches. In such patches, young colonies are able to occur close together as they have a relatively low foraging demand and therefore a low spatial demand. In contrast, their critical distance to taller colonies with higher foraging demands is rather large, which leads to the observed increasing difference of mound heights with increasing distances between them.